Maybe it's my wit and charm, but I haven't had a problem with a dealer mounting parts I've ordered elsewhere. For me it was a Ford dealer, brought brake pads and rotors to them and asked to install, paid them the labor fee and all were happy.

Yes,the local Honda shop is fine with changing tires no matter where they came from,they also have such good deals on tires I buy them there whenever I can.

Its a customer service thing,even if a shop only makes the tire change $ but they do it with a smile,balance the tire correctly, use good wheel weights that dont fly off. It creates more business by doing what a customer needs,said customer might come back and buy something.
Or tell friends "Those guys are great,great shop!"

Being a sourpuss and telling customers that we wont change your tire cant possibly help anything.